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BIM2Arhs.m

## Copyright (C) 2007,2008,2009  Carlo de Falco, Massimiliano Culpo
##
##                   BIM - Box Integration Method Package for Octave
## 
##  BIM is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 2 of the License, or
##  (at your option) any later version.
##
##  BIM is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  You should have received a copy of the GNU General Public License
##  along with BIM; If not, see <http://www.gnu.org/licenses/>.
##
##
##  AUTHORS:
##
##  Carlo de Falco <cdf _AT_ users.sourceforge.net>
##
##  Culpo Massimiliano
##  Bergische Universitaet Wuppertal
##  Fachbereich C - Mathematik und Naturwissenschaften
##  Arbeitsgruppe fuer Angewandte MathematD-42119 Wuppertal  Gaussstr. 20 
##  D-42119 Wuppertal, Germany

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{b}]} = BIM2Arhs(@var{mesh}, @var{f}, @var{g})
##
## Constructs the RHS for the DAR problem
## @iftex 
## @tex
## $ -div ( \alpha  \gamma  ( \eta \vect{\nabla} u - \vect{beta} u )) + \delta \zeta u = f g $
## @end tex 
## @end iftex 
## @ifnottex
## -div (@var{alpha} * @var{gamma} (@var{eta} grad u - @var{beta} u )) + @var{delta} * @var{zeta} u = @var{f}*@var{g}
## @end ifnottex
## 
## Input:
## @itemize @minus
## @item @var{mesh}: PDEtool-like mesh with required field "p", "e", "t".
## @item @var{g}: element-wise constant scalar function.
## @item @var{f}: piecewise linear conforming scalar function.
## @end itemize 
##
## @seealso{BIM2Areaction, BIM2Aadvdiff, BIM2Cmeshproperties}
## @end deftypefn

function b = BIM2Arhs(mesh,f,g)

  Nnodes    =size(mesh.p,2);
  Nelements =size(mesh.t,2);
  
  f       = f(mesh.t(1:3,:));
  wjacdet = mesh.wjacdet;
  ## build local matrix 
  Blocmat=zeros(3,Nelements); 
  for inode=1:3
    Blocmat(inode,:) = g'.*f(inode,:).*wjacdet(inode,:);
  endfor

  gnode=(mesh.t(1:3,:));
  
  ## assemble global matrix
  b = sparse(gnode(:),1,Blocmat(:));

endfunction

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